DEVELOPING ENGINEERING DESIGN CRITERIA FOR MASS GRAVITY
FLOWS IN DEEP OCEAN AND CONTINENTAL SLOPE ENVIRONMENTS
A. W. NIEDORODA, C. W. REED, L. HATCHETT, H. S. DAS
URS Corporation, 3676 Hartsfield, Road, Tallahassee, Florida 32303
Abstract
A series of developments that led to both new understandings of mass gravity flows in
the marine environment and in the techniques to quantitatively analyze them. Methods
have been developed that exploit the newly emerging technical capabilities to perform
very precise and detailed field investigations in deep continental slope settings that
support numerical models which simulate the flows and their deposits. This combination
of technologies provides a means to create engineering design criteria for mass gravity
flows. In this paper, the methods that have been developed for these analyses are
described and illustrated with examples.
Keywords: Mass gravity flows, debris flows, mudflows, turbidity currents,
deep water geohazards
1. Introduction
Advances in construction technologies have brought engineers a growing familiarity
with new challenges from unexpected strong currents, rough and unstable bottom terrain
and a variety of high speed mass gravity flow signatures, showing that these episodic
events are ongoing hazards to design. The body of knowledge that is emerging upon
which engineering design criteria for mass gravity flows are defined, is the subject of
this paper.
2. Background
We use the term mass gravity flows to cover a range of near-bottom sediment flows.
This is a general term because they are applied to uncommon and episodic flows that
have distinctly different physical characteristics. Although we have followed consistent
terminology in a series of publications on these subjects, it is not clear that our terms, or
any others, are universally accepted. We recognize distinct types of flows. These are: 1)
debris flows and mudflows, and 2) turbidity currents.
Debris flows, which we consider to include mudflows, are mass movements in which
the source sediment travels downslope, coming to rest after the initially stored potential
energy is dissipated by friction. During these flows, the source sediment is remolded
and reconstituted; the degree to which this occurs determines the rheological properties
and flow type. The soil mass travels as a visco-plastic material, with distinct stressstrain rate characteristics.
Debris flows are triggered by gravitational soil mass failures which, themselves, can
originate in a number of different ways in the marine environment. These failures are
commonly associated with the steep terrain of the continental slope but can develop on
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gentle slopes where the soils are weak or where mobilizing fluid pressures are present.
Common triggers of gravitational soils failures include: 1) earthquake excitation, 2)
over-thickening or over-steepening due to progressive sedimentation, 3) changes in the
pore pressure regime, 4) progressive steepening of a slope due to creep of underlying
salt layers, and 5) hydrodynamic forcing by strong currents or very large waves
(including internal waves). As noted by Locat and Lee (2002) the sequence of processes
that develop during the brief time that the soil mass is failing is poorly known. In many
but not all cases, a portion of the slide toe becomes remolded, takes on water and flows
downslope as the debris flow. Figure 1 schematically illustrates this sequence.
A turbidity current is a rather different type of near-bed flow. Turbidity currents are
turbulent flows that entrain and suspend bottom sediments. In comparison to the
Figure 1. Schematic of the initial development of a debris flow.
mudflows, their densities are relatively low, with depth-integrated values only 2 percent
to 4 percent above the surrounding water. This increased density is sufficient for the
flows to be accelerated downslope to the point where the gravitational effects are
balanced by drag and the entrainment of zero momentum water from above. Velocities
can exceed 10 m/s, and persistent low-velocity flows also occur. The higher speeds are
adequate to erode and entrain bottom sediments. This adds to the mass of the current,
which tends to increase its speed during its original phase.
Deep ocean mass gravity flows
87
Turbidity currents are also commonly triggered by debris flows. Figure 2 (next page) is
a schematic illustration of a turbidity current originating from a debris flow. In addition
to the triggering events associated with debris flows, turbidity currents can also result
from the discharge of very turbid river water (Mulder and Syvitsky, 1982). Such
bottom-following discharges are rare in the ocean because almost all river plumes are
buoyant due to the salinity and temperature effects that sediment suspension. This is not
the case in fresh water, and long duration turbidity currents are associated with periods
of high river discharge.
3. Approach
Mass gravity flows are important because they often have the strength to damage subsea
structures, pipelines and submarine cables. They are relatively rare episodic events that
are difficult to predict. The approach that we have been following in a sequence of
industrially significant projects recognizes that these flows leave their own long-term
records in the form of sedimentary deposits. Therefore, if suitable rigorous
mathematical models are applied to simulate the observed and measured distribution of
key features of these sedimentary records, then the flow kinematics output from the
models are useful estimators of the time history of actual flows.
Figure 2: Schematic of a turbidity current originating from a debris flow.
4. The Numerical Models
4.1 DEBRIS FLOW/MUDFLOW MODELS
Because the dynamics of both debris flows and mudflows are essentially the same,
within the present limits of measurement and our ability to physically represent these
phenomena, we have used the same models for problems involving both. We have
applied three models. The first one is BING, which was developed at St. Anthony Falls
Laboratory and is based on the model of Jiang and LeBlond (1993) that provides a
Lagrangian representation. Subsequently we have developed the DM-1D and DM-2D
models that operate in a Eulerian framework.
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The DM-1D and DM-2D debris flow mudflow models are based on the thin layer
approximation to the Navier-Stokes and mass continuity equations. The model assumes
that the flow is thin (relative to its length) and that its rheology can be represented as a
Bingham fluid. The one-dimensional model governing equations are:
2
∂uh
∂uuh 1
∂h
∂η
+ρ
+ ( ρ − ρ ′) g
− ( ρ − ρ ′) gh
ρ
−τ = 0
(1)
∂t
∂x
∂x
2
∂x
∂h
+
∂uh
=M
(2)
∂t
∂x
where x is the distance along the profile, t is time, u is the depth-averaged speed, h is the
mudflow height, g is the gravitational acceleration, ρ is the mud bulk density, ρ ′ is
the ambient fluid density (i.e., air or water), η is the bed elevation, τ is the bottom
stress and M is a source term.
The bottom stress τ is determined from the flow kinematics. The model assumes that
the flow consists of an undeformed layer and a deforming layer. The undeformed layer
is the region in which the shear stress is below the yield strength of the mud. This layer
extends from the debris flow upper surface to a critical depth. In the lower region, the
soil mass is assumed to be a viscous fluid with a parabolic velocity profile that extends
from the bed to the base of the undeformed layer. The critical depth is determined from
the force balance equation:
τ c = ( ρ − ρ ′) ghc (
∂η
∂x
−
∂h
∂x
)
which can be solved algebraically for the critical depth hc. The bottom drag stress
τ =µ
∂u
∂z
(3)
τ
is:
(4)
where µ is the kinematic viscosity and z is the vertical coordinate. The velocity
gradient is determined by taking the z-derivative of the fitted velocity profile at the bed.
The profile fit is constrained by a no-flow condition at the bed, and an integral equation
imposing the depth-averaged speed.
The above equations are solved using a Eulerian-based numerical solution method. A
one-dimensional grid, characterized by the grid spacing ∆x , is specified over the
profile. Standard finite-volume solution methods are then used to integrate the
governing equations in time over the profile. The debris flow source can be specified as
an initial block of material located anywhere on the profile (i.e., initial conditions) or by
specifying the location(s) and flow rates for the mud source (i.e., M).
The two-dimensional model is a straightforward extension of the one-dimensional
model:
2
∂uh
∂uuh ∂uvh 1
∂h
∂η
ρ
+ρ
+
+ ( ρ − ρ ′) g
− ( ρ − ρ ′) gh
−τ x = 0
∂t
∂x
∂y
2
∂x
∂x
(5)
Deep ocean mass gravity flows
ρ
∂vh
∂h
∂t
∂t
+
∂vuh
+ρ
∂uh
∂x
∂x
+
∂vh
∂y
+
∂vvh
∂y
+
1
2
( ρ − ρ ′) g
∂h
2
∂y
− ( ρ − ρ ′) gh
=M
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∂η
∂y
−τ y = 0
(6)
(7)
where v is the y-direction velocity component and the bottom stress now has both x and
y components (noted with x and y subscripts). The critical depth is calculated using the
equation:
τ c = ( ρ − ρ ′) ghc ∇ (η − h )
where
(8)
indicate the magnitude of the vector quantity and ∇ is the gradient operator.
The bottom stress components are determined as:
τx = µ
τy =µ
∂u
∂z
(9)
∂v
(10)
∂z
where, as for the one-dimensional model, the derivatives are obtained form a parabolic
velocity profile. In the two-dimensional case, the profiles are fitted independently for
the x and y velocity components.
The same standard finite-volume numerical solution methods that are used in the onedimensional model are used for the two-dimensional model. The grid now is
characterized by both an x-direction spacing, ∆x and a y-direction spacing, ∆y . Both
“initial block” conditions and source conditions (M) can be specified for the twodimensional model.
4.2 TURBIDITY CURRENT MODELS
There are two types of turbidity current models that we have applied. One represents a
width-averaged flow in a vertical section along the thalweg of a flow channel. This
model is described in Reed et al. (2000). The other represents a two-dimensional flow
in plan view. This is capable of resolving details of flow and sedimentation in the
winding channels that characterize numerous large submarine canyon systems.
4.3 A MECHANISTIC MODEL OF SUBMARINE CHANNEL MIGRATION
(SUBMEANDERR)
We have developed another numerical for turbidity currents to evaluate the flow
behavior and sediment response in detailed reaches of meandering channels. This
numerical model (SUBMEANDERR) is based on the recent progress in quantifying the
initiation and migration of meander bends in rivers. This model allows for the exchange
of sediment between the bed and the current along a channel of arbitrary planform. It
uses transient depth-averaged equations describing mass, momentum and turbulent
kinetic energy of fluid and the conservation of sediment (suspended and bed load).
These equations are cast in an intrinsic coordinate system and solved in conjunction
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with the Exner equation for bed sediment continuity using an explicit finite-difference
scheme.
5. Field Programs
The robust numerical models described above become useful tools when they are
combined with adequate measurements of actual seafloor features and deposits. The
field program is usually divided into three parts. First there is a reconnaissance survey
that explores the area. This often depends on exploitation of pre-existing survey data.
The data and maps acquired in the reconnaissance phase are reviewed and a preliminary
map of slide scars, faults, steep slopes, debris flow deposits and evidence of turbidity
current features such as canyons, channels and over-bank deposits are located in relation
to the places where wells, pipelines or other seafloor structures may be required. In
some cases it is possible to make initial uncalibrated modeling analyses based on the
reconnaissance-level data to explore the general characteristics of mass gravity flows in
the general terrain of the project area.
The second part of the field program usually consists of a carefully planned geophysical
survey. Where adequate data have been acquired in the reconnaissance phase it is
possible to specify exact locations to be measured and trackline densities that are
needed. Surveys to evaluate mass gravity flow geohazards differ from many other types
of surveys because it is necessary to understand the natural features of the project area.
The source area of mass gravity flows can be located far up slope. The places where
deposits that can be sampled and used to constrain the numerical models can be located
far downslope. Accordingly, the geophysical surveys are usually organized to cover the
natural features rather than specific locations of facility foundations or pipeline routes.
The third component of the field survey is a bottom sampling program. Usually three
types of sampling are required. Deep borings are often necessary to analyze the stability
of large-scale features. Long sediment cores are taken to understand the shallow
stratigraphy, identify event beds, and provide a sequence of sediment samples. Box
cores are typically used to sample the seabed for detailed determination of the sediment
properties. These cores are subsampled as soon as they are returned to the deck.
6. Laboratory Analyses
6.1 CORE DESCRIPTIONS AND SAMPLING
Accurate and detailed descriptions of the sediment cores are a key part of the analysis
process. The descriptions need to be specially tailored to the needs of the numerical
modeling. Transmission X-ray imagery has also proved to be useful in distinguishing
the nature and thickness of many event beds in sediment cores.
6.2 AGE DATING
The recurrence rate of mass gravity flows is to obtain from a series of nuclear age dates
in sediment cores that contain a sequence of beds created by earlier events. Samples that
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91
are to be dated come from the pelagic sediment layers that are found between event
beds. The event beds themselves are comprised of reworked sediments from previous
deposits so that their apparent age dates are not useful. Dating is based on the relative
activity of C14 is commonly used because marine sediments often have sufficient
inventories of carbon from organic material that is part of the “pelagic rain” or occurs in
micro-fossils. The age range for C14 dating lies between 35,000 and a few hundred
years.
6.3 GRAIN SIZE DETERMINATIONS
Grain size data from standard analyses are needed as inputs to the turbidity current
model.
6.4 EROSION TESTING
The passage of a turbidity current depends on an exchange of sediment with the bed. To
model this process, it is necessary to know the erosion rate and the minimum tractive
stress needed to entrain the bed sediment.
To determine the erosion threshold stress and the erosion rate as a function of the
boundary fluid stress above this limit, it is necessary to make measurements in flumes.
Subsamples from box cores are tested in a special flume at the St. Anthony Falls
Hydraulic Laboratory or at the Civil Engineering Department at Texas A & M
University.
7. Diagnostic Modeling And Model Calibration
In the diagnostic modeling phase of the project all of the relevant data are brought to
bear on understanding and properly simulating the evidence of past events. We have
found that this usually requires the coordinated efforts of an experienced technical team
consisting of individuals with diverse backgrounds.
7.1 CALIBRATION OF DEBRIS FLOW AND MUDFLOW MODELS
Existing debris flows and/or mudflows are detected and mapped from the geophysical
data. These may occur on the seafloor or be buried beneath. They are often composite
deposits and it is necessary to make detailed determinations of how many individual
events lie within.
The field measurements are combined for distinct modeling scenarios. The shape of the
bottom profile before the event is determined from the bathymetric and sub-bottom data.
The length, width, height and shape of the flow are measured. Where possible the
sedimentary and geotechnical properties of the flow are determined from sediment
cores.
The modeling scenario is not complete without information about the triggering event.
Where possible the failure headwall and slump deposits are measured. If this is not
possible, then these are back-calculated from the volume and geometry of the debris
flow.
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7.2 CALIBRATION OF THE TURBIDITY CURRENT MODELS
There are many features that are combined to create modeling scenarios for turbidity
currents. Modeling scenarios for turbidity currents consist of the initial conditions,
boundary conditions, and model parameters that need to be specified. Usually, the initial
conditions are quiescent ambient conditions throughout the domain (no background
current all along the feature), with no initial suspended sediment. Boundaries consist of
flow velocity (Uo), flow height (Ho), and an initial concentration (Coi) for each
sediment size class. These conditions may vary over time or be continuous.
The model parameters requiring specification are the bed slope (θ), the erosion
parameters [E, b(τb)], the settling velocities wsi, the critical stress for erosion τci, the
sediment size distribution fi, and the bottom roughness coefficient (zo). The bed slope is
obtained from the bathymetric maps. The two parameters that influence sediment
erosion, E and b(τb), are to be determined from laboratory flume measurements.
Depending on the situation, there are a number of possible constraints that can be used
to assess the behavior of the turbidity current model. It should reproduce the length of
the zone of erosion, and it should develop a bed stress above the limit for entrainment of
bedload for the entire length of the channel where medium sands and coarser sediment
are observed, the transition from a sand bed to a silty bed should occur near the same
place, and the flow heights should exceed the levee heights.
Another element of the diagnostic phase of a project is the determination of the ages of
past flows. The most complete records come from cores taken in the run-out zone.
However, small events may not be recorded this far down the system so that the levees
should be sampled as well. The number of events in the time intervals is then used to
compute the return periods.
8. Prognostic Modeling And Recurrence Interval Analysis
The prognostic modeling phase of a project is carried out to predict the locations where
future mass gravity flows may occur and to evaluate the severity of these events
according to their projected recurrence intervals. Depending on the setting, the interest
may be with debris flows, mudflows, turbidity currents or any combination of these
phenomena. Because these events are routed down predictable gravity-controlled flow
paths, the hazards are very site specific.
For the purpose of explanation we will take the case of a local slope failure, triggered by
earthquake activity, that causes a debris flow and a turbidity current. The recurrence
interval statistics of an earthquake climate are determined from seismological data.
Using ground acceleration and duration data for various recurrence intervals, the size of
the gravitational soil failures can be evaluated with normal geotechnical slope stability
relationships. The field observations are used to relate the size of the whole soil mass
failure to the volume of material that becomes the debris flow. The calibrated model is
then run to evaluate the run-out length and profile of maximum speed along its flow
path. Figure 3 shows an example of the model results. The speed predicted for this large
Deep ocean mass gravity flows
93
Figure 3: Example of prognostic model output for a debris flow.
flow has maximum values of 17 m/s. These speeds are consistent with observed
terrestrial debris flows and mudflows.
The seafloor record is used to predict future behavior of turbidity currents. Event
deposits are usually a few millimeters to a few centimeters thick, although there are
occasions when dramatic beds on the order of a meter in thickness are encountered. The
typical thickness of event beds means that a large population of events can be
documented within the normal length of piston or gravity cores. With appropriate dating
of the intervening layers of pelagic sediments, a chronology of events can be
established. This leads to the development of a number of model scenarios based on the
spatial arrangement of sediment grain sizes and the thickness of event beds that
characterize the different levels of event severity. In concept these are the 1,000-year,
100-year, etc. event scenarios. In actuality the intervals are more irregular. The model is
then used to simulate the depositional regimes for each of these scenarios. Computed
profiles of current speed, density and other parameters are output for the specific point
(or points) of interest along the channel. Figure 4 shows an example of this output.
Where detailed data concerning the depositional portions of the turbidity currents
systems are not available, it is possible to conduct a similar analysis based on
information on the magnitudes and recurrence intervals of the triggering events. We
have adapted the turbidity current model to contain a “moving seafloor” in a portion of
the upper bathymetric profile. This simulates a debris flow. The debris flows are
modeled separately, and their flow characteristics are part of the input to the turbidity
current model.
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9. Summary
Advances in deep water marine survey capabilities and the development of robust
numerical models of mass gravity flows are combined in a methodology that permits
engineering design criteria for mudflows, debris flows and turbidity currents. One set of
numerical models has been described in this paper, as have several of the milestones in
deep water high-resolution geophysical surveying techniques. The examples given in
this paper show how the method components are applied. The emergence of these
applications of marine geophysics and geology can provide guidance for future research,
which is needed to further advance our knowledge of these significant geohazards.
Figure 4: Example of outputs from turbidity current models.
10. Acknowledgements
Some of the costs for the preparation of this manuscript were provided by the Office of
Naval Research Eurostrataform Project.
11. References
Jiang, L. and P.H. LeBlond. 1993. Numerical modeling of an underwater Bingham plastic mudslide and the
waves which it generates. J. Geophysical Research. p.10303-10317.
Locat, J. and H.J. Lee. 2002. Submarine landslides: advances and challenges. Can. Geotech J., v. 39, p. 192212.
Mulder, T. and J. P.M. Syvitsky. 1982. Turbidity currents generated from river mouths during exceptional
discharges to the world oceans. J. Geol., v. 103, p. 285-299.
Reed, C.W., Niedoroda, A.W., Parker, G., Gelfembaum, G. and C. Dalton. 2000. Predicting turbidity current
speeds using numerical models. 19th Int’l OMAE Confr. Proceedings.